Can 'to' be used instead of 'in'?

I suspect there might be a difference in usage between American English and British English, which is also used, in one form or another, around the world. As an American though, I'll take a stab at it.
An appeal in the High Court would tend to imply the High Court has agreed to hear the appeal already and is preparing to do so, or the appeal is already accepted and is being heard. An appeal to the High Court would seem to apply that an application to argue an appeal has been made, but that application has not yet been accepted and the appeal might or might not ever be heard.

No legal scholar here, but that's what it sounds like to me.

In Canada in is the correct word for the context you provided.